Problem: Find the distance between the points (5, -6) and (1, 4). ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(5, -6)$ $(1, 4)$ $4$ $10$
Solution: Change in $x$ Change in $y$ (-6) 10 The distance is the length of the hypotenuse of this right triangle. By the Pythagorean Theorem, that length is equal to: $\sqrt{4^2 + 10^2}$ $= \sqrt{116}$ $= 2\sqrt{29}$